MULTIPLE Lp ANALYTIC GENERALIZED FOURIER-FEYNMAN TRANSFORM ON THE BANACH ALGEBRA

Title & Authors
MULTIPLE Lp ANALYTIC GENERALIZED FOURIER-FEYNMAN TRANSFORM ON THE BANACH ALGEBRA
Chang, Seung-Jun; Choi, Jae-Gil;

Abstract
In this paper, we use a generalized Brownian motion process to define a generalized Feynman integral and a generalized Fourier-Feynman transform. We also define the concepts of the multiple Lp analytic generalized Fourier-Feynman transform and the generalized convolution product of functional on function space $\small{C_{a,\;b}[0,\;T]}$. We then verify the existence of the multiple $\small{L_{p}}$ analytic generalized Fourier-Feynman transform for functional on function space that belong to a Banach algebra $\small{S({L_{a,\;b}}^{2}[0, T])}$. Finally we establish some relationships between the multiple $\small{L_{p}}$ analytic generalized Fourier-Feynman transform and the generalized convolution product for functionals in $\small{S({L_{a,\;b}}^{2}[0, T])}$.ﾖ⨀
Keywords
generalized Brownian motion process;generalized analytic Feynman integral;generalized analytic Fourier-Feynman transform;generalized convolution product;multiple $\small{L_{p}}$ analytic generalized fourier-Feynman transform;
Language
English
Cited by
1.
CONDITIONAL GENERALIZED FOURIER-FEYNMAN TRANSFORM OF FUNCTIONALS IN A FRESNEL TYPE CLASS,;

대한수학회논문집, 2011. vol.26. 2, pp.273-289
2.
GENERALIZED ANALYTIC FOURIER-FEYNMAN TRANSFORMS AND CONVOLUTIONS ON A FRESNEL TYPE CLASS,;;

대한수학회보, 2011. vol.48. 2, pp.223-245
3.
CHANGE OF SCALE FORMULAS FOR FUNCTION SPACE INTEGRALS RELATED WITH FOURIER-FEYNMAN TRANSFORM AND CONVOLUTION ON Ca,b[0, T],;;;

Korean Journal of Mathematics, 2015. vol.23. 1, pp.47-64
1.
CONDITIONAL GENERALIZED FOURIER-FEYNMAN TRANSFORM OF FUNCTIONALS IN A FRESNEL TYPE CLASS, Communications of the Korean Mathematical Society, 2011, 26, 2, 273
2.
GENERALIZED ANALYTIC FOURIER-FEYNMAN TRANSFORMS AND CONVOLUTIONS ON A FRESNEL TYPE CLASS, Bulletin of the Korean Mathematical Society, 2011, 48, 2, 223
3.
CHANGE OF SCALE FORMULAS FOR FUNCTION SPACE INTEGRALS RELATED WITH FOURIER-FEYNMAN TRANSFORM AND CONVOLUTION ON Ca,b[0, T], Korean Journal of Mathematics, 2015, 23, 1, 47
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